\documentclass[9pt]{article}
\usepackage{amsmath}
\begin{document}
Read in the following dictionary:
\[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{10}   &  -22.0 & +  4.00 x_{1} & +  9.00 x_{2} & +  2.00 x_{3} & +  4.00 x_{4} & +  6.00 x_{5} & +  3.00 x_{6} & -1.00 x_{7} & -3.00 x_{8} & -6.00 x_{9}\\
 x_{11}   &  42.0 & +  4.00 x_{1} & -5.00 x_{2} & -5.00 x_{3} & +  2.00 x_{4} &   & -7.00 x_{6} & -8.00 x_{7} & -5.00 x_{8} & +  7.00 x_{9}\\
 x_{12}   &  0.0 & -9.00 x_{1} & +  2.00 x_{2} & -2.00 x_{3} & +  4.00 x_{4} & +  5.00 x_{5} & -7.00 x_{6} & +  6.00 x_{7} & -2.00 x_{8} & -2.00 x_{9}\\
 x_{13}   &  11.0 & -7.00 x_{1} & -3.00 x_{2} & -1.00 x_{3} & +  4.00 x_{4} & +  1.00 x_{5} & -4.00 x_{6} & -4.00 x_{7} & +  8.00 x_{8} & -2.00 x_{9}\\
 x_{14}   &  -1.0 & +  8.00 x_{1} & +  9.00 x_{2} & +  6.00 x_{3} & +  7.00 x_{4} & -4.00 x_{5} & -7.00 x_{6} & +  7.00 x_{7} & -4.00 x_{8} & -9.00 x_{9}\\
 x_{15}   &  47.0 & +  9.00 x_{1} & +  5.00 x_{2} & -7.00 x_{3} & -10.00 x_{4} & -3.00 x_{5} & +  1.00 x_{6} & +  3.00 x_{7} & +  3.00 x_{8} & +  8.00 x_{9}\\
 x_{16}   &  -37.0 & -1.00 x_{1} & + 10.00 x_{2} & +  8.00 x_{3} & -1.00 x_{4} & +  7.00 x_{5} & +  1.00 x_{6} & +  6.00 x_{7} & -6.00 x_{8} & -1.00 x_{9}\\
 x_{17}   &  -1.0 & +  7.00 x_{1} & +  5.00 x_{2} & + 10.00 x_{3} & +  6.00 x_{4} & -10.00 x_{5} & -2.00 x_{6} & -5.00 x_{7} & -1.00 x_{8} & +  5.00 x_{9}\\
 x_{18}   &  36.0 & -8.00 x_{1} & +  3.00 x_{2} & +  2.00 x_{3} & -2.00 x_{4} & -3.00 x_{5} & -10.00 x_{6} & +  3.00 x_{7} & -2.00 x_{8} & +  2.00 x_{9}\\
\hline
z    &  0.0 & -1.00 x_{1} & +  1.00 x_{2} & +  4.00 x_{3} & -4.00 x_{4} & -4.00 x_{5} & -3.00 x_{6} & -3.00 x_{7} & +  2.00 x_{8} & +  4.00 x_{9}\\
\end{array}\]
\subsection{Initialization Phase: Dual Problem Solving}
New Objective in primal was changed to : \[ \max\ \sum_{j=1}^{9}\ - x_j \] 
Primal variable $x_j$ corresponds to dual variable $y_j$ for $j = 1,\ldots,18$
Dual Dictionary (with objective changed is): 
\[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 y_{1}   &  1.0 & -4.00 y_{10} & -4.00 y_{11} & +  9.00 y_{12} & +  7.00 y_{13} & -8.00 y_{14} & -9.00 y_{15} & +  1.00 y_{16} & -7.00 y_{17} & +  8.00 y_{18}\\
 y_{2}   &  1.0 & -9.00 y_{10} & +  5.00 y_{11} & -2.00 y_{12} & +  3.00 y_{13} & -9.00 y_{14} & -5.00 y_{15} & -10.00 y_{16} & -5.00 y_{17} & -3.00 y_{18}\\
 y_{3}   &  1.0 & -2.00 y_{10} & +  5.00 y_{11} & +  2.00 y_{12} & +  1.00 y_{13} & -6.00 y_{14} & +  7.00 y_{15} & -8.00 y_{16} & -10.00 y_{17} & -2.00 y_{18}\\
 y_{4}   &  1.0 & -4.00 y_{10} & -2.00 y_{11} & -4.00 y_{12} & -4.00 y_{13} & -7.00 y_{14} & + 10.00 y_{15} & +  1.00 y_{16} & -6.00 y_{17} & +  2.00 y_{18}\\
 y_{5}   &  1.0 & -6.00 y_{10} &   & -5.00 y_{12} & -1.00 y_{13} & +  4.00 y_{14} & +  3.00 y_{15} & -7.00 y_{16} & + 10.00 y_{17} & +  3.00 y_{18}\\
 y_{6}   &  1.0 & -3.00 y_{10} & +  7.00 y_{11} & +  7.00 y_{12} & +  4.00 y_{13} & +  7.00 y_{14} & -1.00 y_{15} & -1.00 y_{16} & +  2.00 y_{17} & + 10.00 y_{18}\\
 y_{7}   &  1.0 & +  1.00 y_{10} & +  8.00 y_{11} & -6.00 y_{12} & +  4.00 y_{13} & -7.00 y_{14} & -3.00 y_{15} & -6.00 y_{16} & +  5.00 y_{17} & -3.00 y_{18}\\
 y_{8}   &  1.0 & +  3.00 y_{10} & +  5.00 y_{11} & +  2.00 y_{12} & -8.00 y_{13} & +  4.00 y_{14} & -3.00 y_{15} & +  6.00 y_{16} & +  1.00 y_{17} & +  2.00 y_{18}\\
 y_{9}   &  1.0 & +  6.00 y_{10} & -7.00 y_{11} & +  2.00 y_{12} & +  2.00 y_{13} & +  9.00 y_{14} & -8.00 y_{15} & +  1.00 y_{16} & -5.00 y_{17} & -2.00 y_{18}\\
\hline
z    &  -0 & + 22.00 y_{10} & -42.00 y_{11} &   & -11.00 y_{13} & +  1.00 y_{14} & -47.00 y_{15} & + 37.00 y_{16} & +  1.00 y_{17} & -36.00 y_{18}\\
\end{array}\]
Initialization succeeded in finding final dual dictionary with 4 pivots
\[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 y_{1}   &  1.8064516129 & +  1.55 y_{2} & -11.74 y_{11} & +  0.32 y_{12} & -2.35 y_{5} & + 15.35 y_{14} & +  5.81 y_{15} & -4.19 y_{10} & + 24.29 y_{17} & + 19.71 y_{18}\\
 y_{16}   &  0.129032258065 & -0.03 y_{2} & +  0.16 y_{11} & -0.55 y_{12} & -0.10 y_{5} & +  0.10 y_{14} & +  0.13 y_{15} & -0.87 y_{10} & +  0.81 y_{17} & +  0.19 y_{18}\\
 y_{3}   &  0.0645161290323 & +  0.48 y_{2} & +  2.58 y_{11} & +  5.23 y_{12} & +  0.45 y_{5} & -3.45 y_{14} & +  8.06 y_{15} & +  5.06 y_{10} & -12.10 y_{17} & -1.90 y_{18}\\
 y_{4}   &  0.741935483871 & -0.94 y_{2} & +  2.68 y_{11} & +  0.10 y_{12} & +  1.19 y_{5} & -20.19 y_{14} & +  1.74 y_{15} & -5.26 y_{10} & -22.61 y_{17} & -4.39 y_{18}\\
 y_{13}   &  0.0967741935484 & +  0.23 y_{2} & -1.13 y_{11} & -1.16 y_{12} & -0.32 y_{5} & +  3.32 y_{14} & +  2.10 y_{15} & +  0.10 y_{10} & +  4.35 y_{17} & +  1.65 y_{18}\\
 y_{6}   &  1.25806451613 & +  0.94 y_{2} & +  2.32 y_{11} & +  2.90 y_{12} & -1.19 y_{5} & + 20.19 y_{14} & +  7.26 y_{15} & -1.74 y_{10} & + 18.61 y_{17} & + 16.39 y_{18}\\
 y_{7}   &  0.612903225806 & +  1.10 y_{2} & +  2.52 y_{11} & -7.35 y_{12} & -0.71 y_{5} & +  5.71 y_{14} & +  4.61 y_{15} & +  6.61 y_{10} & + 17.58 y_{17} & +  2.42 y_{18}\\
 y_{8}   &  1.0 & -2.00 y_{2} & + 15.00 y_{11} & +  8.00 y_{12} & +  2.00 y_{5} & -22.00 y_{14} & -19.00 y_{15} & -3.00 y_{10} & -29.00 y_{17} & -10.00 y_{18}\\
 y_{9}   &  1.32258064516 & +  0.42 y_{2} & -9.10 y_{11} & -0.87 y_{12} & -0.74 y_{5} & + 15.74 y_{14} & -3.68 y_{15} & +  5.32 y_{10} & +  4.52 y_{17} & +  1.48 y_{18}\\
\hline
z    &  3.70967741935 & -3.68 y_{2} & -23.61 y_{11} & -7.52 y_{12} & -0.03 y_{5} & -31.97 y_{14} & -65.29 y_{15} & -11.29 y_{10} & -17.06 y_{17} & -46.94 y_{18}\\
\end{array}\]
Primal Dictionary is:
\[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{2}   &  3.67741935484 & -1.55 x_{1} & +  0.03 x_{16} & -0.48 x_{3} & +  0.94 x_{4} & -0.23 x_{13} & -0.94 x_{6} & -1.10 x_{7} & +  2.00 x_{8} & -0.42 x_{9}\\
 x_{11}   &  23.6129032258 & + 11.74 x_{1} & -0.16 x_{16} & -2.58 x_{3} & -2.68 x_{4} & +  1.13 x_{13} & -2.32 x_{6} & -2.52 x_{7} & -15.00 x_{8} & +  9.10 x_{9}\\
 x_{12}   &  7.51612903226 & -0.32 x_{1} & +  0.55 x_{16} & -5.23 x_{3} & -0.10 x_{4} & +  1.16 x_{13} & -2.90 x_{6} & +  7.35 x_{7} & -8.00 x_{8} & +  0.87 x_{9}\\
 x_{5}   &  0.0322580645161 & +  2.35 x_{1} & +  0.10 x_{16} & -0.45 x_{3} & -1.19 x_{4} & +  0.32 x_{13} & +  1.19 x_{6} & +  0.71 x_{7} & -2.00 x_{8} & +  0.74 x_{9}\\
 x_{14}   &  31.9677419355 & -15.35 x_{1} & -0.10 x_{16} & +  3.45 x_{3} & + 20.19 x_{4} & -3.32 x_{13} & -20.19 x_{6} & -5.71 x_{7} & + 22.00 x_{8} & -15.74 x_{9}\\
 x_{15}   &  65.2903225806 & -5.81 x_{1} & -0.13 x_{16} & -8.06 x_{3} & -1.74 x_{4} & -2.10 x_{13} & -7.26 x_{6} & -4.61 x_{7} & + 19.00 x_{8} & +  3.68 x_{9}\\
 x_{10}   &  11.2903225806 & +  4.19 x_{1} & +  0.87 x_{16} & -5.06 x_{3} & +  5.26 x_{4} & -0.10 x_{13} & +  1.74 x_{6} & -6.61 x_{7} & +  3.00 x_{8} & -5.32 x_{9}\\
 x_{17}   &  17.064516129 & -24.29 x_{1} & -0.81 x_{16} & + 12.10 x_{3} & + 22.61 x_{4} & -4.35 x_{13} & -18.61 x_{6} & -17.58 x_{7} & + 29.00 x_{8} & -4.52 x_{9}\\
 x_{18}   &  46.935483871 & -19.71 x_{1} & -0.19 x_{16} & +  1.90 x_{3} & +  4.39 x_{4} & -1.65 x_{13} & -16.39 x_{6} & -2.42 x_{7} & + 10.00 x_{8} & -1.48 x_{9}\\
\hline
z    &  -3.70967741935 & -1.81 x_{1} & -0.13 x_{16} & -0.06 x_{3} & -0.74 x_{4} & -0.10 x_{13} & -1.26 x_{6} & -0.61 x_{7} & -1.00 x_{8} & -1.32 x_{9}\\
\end{array}\]
Primal Dictionary with original objective is:
\[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{2}   &  3.67741935484 & -1.55 x_{1} & +  0.03 x_{16} & -0.48 x_{3} & +  0.94 x_{4} & -0.23 x_{13} & -0.94 x_{6} & -1.10 x_{7} & +  2.00 x_{8} & -0.42 x_{9}\\
 x_{11}   &  23.6129032258 & + 11.74 x_{1} & -0.16 x_{16} & -2.58 x_{3} & -2.68 x_{4} & +  1.13 x_{13} & -2.32 x_{6} & -2.52 x_{7} & -15.00 x_{8} & +  9.10 x_{9}\\
 x_{12}   &  7.51612903226 & -0.32 x_{1} & +  0.55 x_{16} & -5.23 x_{3} & -0.10 x_{4} & +  1.16 x_{13} & -2.90 x_{6} & +  7.35 x_{7} & -8.00 x_{8} & +  0.87 x_{9}\\
 x_{5}   &  0.0322580645161 & +  2.35 x_{1} & +  0.10 x_{16} & -0.45 x_{3} & -1.19 x_{4} & +  0.32 x_{13} & +  1.19 x_{6} & +  0.71 x_{7} & -2.00 x_{8} & +  0.74 x_{9}\\
 x_{14}   &  31.9677419355 & -15.35 x_{1} & -0.10 x_{16} & +  3.45 x_{3} & + 20.19 x_{4} & -3.32 x_{13} & -20.19 x_{6} & -5.71 x_{7} & + 22.00 x_{8} & -15.74 x_{9}\\
 x_{15}   &  65.2903225806 & -5.81 x_{1} & -0.13 x_{16} & -8.06 x_{3} & -1.74 x_{4} & -2.10 x_{13} & -7.26 x_{6} & -4.61 x_{7} & + 19.00 x_{8} & +  3.68 x_{9}\\
 x_{10}   &  11.2903225806 & +  4.19 x_{1} & +  0.87 x_{16} & -5.06 x_{3} & +  5.26 x_{4} & -0.10 x_{13} & +  1.74 x_{6} & -6.61 x_{7} & +  3.00 x_{8} & -5.32 x_{9}\\
 x_{17}   &  17.064516129 & -24.29 x_{1} & -0.81 x_{16} & + 12.10 x_{3} & + 22.61 x_{4} & -4.35 x_{13} & -18.61 x_{6} & -17.58 x_{7} & + 29.00 x_{8} & -4.52 x_{9}\\
 x_{18}   &  46.935483871 & -19.71 x_{1} & -0.19 x_{16} & +  1.90 x_{3} & +  4.39 x_{4} & -1.65 x_{13} & -16.39 x_{6} & -2.42 x_{7} & + 10.00 x_{8} & -1.48 x_{9}\\
\hline
z    &  3.54838709677 & -11.97 x_{1} & -0.35 x_{16} & +  5.32 x_{3} & +  1.71 x_{4} & -1.52 x_{13} & -8.71 x_{6} & -6.94 x_{7} & + 12.00 x_{8} & +  0.61 x_{9}\\
\end{array}\]
\section{Optimization Phase Simplex}
Starting Dictionary is:
\[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{2}   &  3.67741935484 & -1.55 x_{1} & +  0.03 x_{16} & -0.48 x_{3} & +  0.94 x_{4} & -0.23 x_{13} & -0.94 x_{6} & -1.10 x_{7} & +  2.00 x_{8} & -0.42 x_{9}\\
 x_{11}   &  23.6129032258 & + 11.74 x_{1} & -0.16 x_{16} & -2.58 x_{3} & -2.68 x_{4} & +  1.13 x_{13} & -2.32 x_{6} & -2.52 x_{7} & -15.00 x_{8} & +  9.10 x_{9}\\
 x_{12}   &  7.51612903226 & -0.32 x_{1} & +  0.55 x_{16} & -5.23 x_{3} & -0.10 x_{4} & +  1.16 x_{13} & -2.90 x_{6} & +  7.35 x_{7} & -8.00 x_{8} & +  0.87 x_{9}\\
 x_{5}   &  0.0322580645161 & +  2.35 x_{1} & +  0.10 x_{16} & -0.45 x_{3} & -1.19 x_{4} & +  0.32 x_{13} & +  1.19 x_{6} & +  0.71 x_{7} & -2.00 x_{8} & +  0.74 x_{9}\\
 x_{14}   &  31.9677419355 & -15.35 x_{1} & -0.10 x_{16} & +  3.45 x_{3} & + 20.19 x_{4} & -3.32 x_{13} & -20.19 x_{6} & -5.71 x_{7} & + 22.00 x_{8} & -15.74 x_{9}\\
 x_{15}   &  65.2903225806 & -5.81 x_{1} & -0.13 x_{16} & -8.06 x_{3} & -1.74 x_{4} & -2.10 x_{13} & -7.26 x_{6} & -4.61 x_{7} & + 19.00 x_{8} & +  3.68 x_{9}\\
 x_{10}   &  11.2903225806 & +  4.19 x_{1} & +  0.87 x_{16} & -5.06 x_{3} & +  5.26 x_{4} & -0.10 x_{13} & +  1.74 x_{6} & -6.61 x_{7} & +  3.00 x_{8} & -5.32 x_{9}\\
 x_{17}   &  17.064516129 & -24.29 x_{1} & -0.81 x_{16} & + 12.10 x_{3} & + 22.61 x_{4} & -4.35 x_{13} & -18.61 x_{6} & -17.58 x_{7} & + 29.00 x_{8} & -4.52 x_{9}\\
 x_{18}   &  46.935483871 & -19.71 x_{1} & -0.19 x_{16} & +  1.90 x_{3} & +  4.39 x_{4} & -1.65 x_{13} & -16.39 x_{6} & -2.42 x_{7} & + 10.00 x_{8} & -1.48 x_{9}\\
\hline
z    &  3.54838709677 & -11.97 x_{1} & -0.35 x_{16} & +  5.32 x_{3} & +  1.71 x_{4} & -1.52 x_{13} & -8.71 x_{6} & -6.94 x_{7} & + 12.00 x_{8} & +  0.61 x_{9}\\
\end{array}\]


 $ x_{3} $ enters and $ x_{5} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{2}   &  3.64285714286 & -4.07 x_{1} & -0.07 x_{16} & +  1.07 x_{5} & +  2.21 x_{4} & -0.57 x_{13} & -2.21 x_{6} & -1.86 x_{7} & +  4.14 x_{8} & -1.21 x_{9}\\
 x_{11}   &  23.4285714286 & -1.71 x_{1} & -0.71 x_{16} & +  5.71 x_{5} & +  4.14 x_{4} & -0.71 x_{13} & -9.14 x_{6} & -6.57 x_{7} & -3.57 x_{8} & +  4.86 x_{9}\\
 x_{12}   &  7.14285714286 & -27.57 x_{1} & -0.57 x_{16} & + 11.57 x_{5} & + 13.71 x_{4} & -2.57 x_{13} & -16.71 x_{6} & -0.86 x_{7} & + 15.14 x_{8} & -7.71 x_{9}\\
 x_{3}   &  0.0714285714286 & +  5.21 x_{1} & +  0.21 x_{16} & -2.21 x_{5} & -2.64 x_{4} & +  0.71 x_{13} & +  2.64 x_{6} & +  1.57 x_{7} & -4.43 x_{8} & +  1.64 x_{9}\\
 x_{14}   &  32.2142857143 & +  2.64 x_{1} & +  0.64 x_{16} & -7.64 x_{5} & + 11.07 x_{4} & -0.86 x_{13} & -11.07 x_{6} & -0.29 x_{7} & +  6.71 x_{8} & -10.07 x_{9}\\
 x_{15}   &  64.7142857143 & -47.86 x_{1} & -1.86 x_{16} & + 17.86 x_{5} & + 19.57 x_{4} & -7.86 x_{13} & -28.57 x_{6} & -17.29 x_{7} & + 54.71 x_{8} & -9.57 x_{9}\\
 x_{10}   &  10.9285714286 & -22.21 x_{1} & -0.21 x_{16} & + 11.21 x_{5} & + 18.64 x_{4} & -3.71 x_{13} & -11.64 x_{6} & -14.57 x_{7} & + 25.43 x_{8} & -13.64 x_{9}\\
 x_{17}   &  17.9285714286 & + 38.79 x_{1} & +  1.79 x_{16} & -26.79 x_{5} & -9.36 x_{4} & +  4.29 x_{13} & + 13.36 x_{6} & +  1.43 x_{7} & -24.57 x_{8} & + 15.36 x_{9}\\
 x_{18}   &  47.0714285714 & -9.79 x_{1} & +  0.21 x_{16} & -4.21 x_{5} & -0.64 x_{4} & -0.29 x_{13} & -11.36 x_{6} & +  0.57 x_{7} & +  1.57 x_{8} & +  1.64 x_{9}\\
\hline
z    &  3.92857142857 & + 15.79 x_{1} & +  0.79 x_{16} & -11.79 x_{5} & -12.36 x_{4} & +  2.29 x_{13} & +  5.36 x_{6} & +  1.43 x_{7} & -11.57 x_{8} & +  9.36 x_{9}\\
\end{array}\]


 $ x_{1} $ enters and $ x_{12} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{2}   &  2.58808290155 & +  0.15 x_{12} & +  0.01 x_{16} & -0.64 x_{5} & +  0.19 x_{4} & -0.19 x_{13} & +  0.25 x_{6} & -1.73 x_{7} & +  1.91 x_{8} & -0.08 x_{9}\\
 x_{11}   &  22.9844559585 & +  0.06 x_{12} & -0.68 x_{16} & +  4.99 x_{5} & +  3.29 x_{4} & -0.55 x_{13} & -8.10 x_{6} & -6.52 x_{7} & -4.51 x_{8} & +  5.34 x_{9}\\
 x_{1}   &  0.259067357513 & -0.04 x_{12} & -0.02 x_{16} & +  0.42 x_{5} & +  0.50 x_{4} & -0.09 x_{13} & -0.61 x_{6} & -0.03 x_{7} & +  0.55 x_{8} & -0.28 x_{9}\\
 x_{3}   &  1.42227979275 & -0.19 x_{12} & +  0.11 x_{16} & -0.03 x_{5} & -0.05 x_{4} & +  0.23 x_{13} & -0.52 x_{6} & +  1.41 x_{7} & -1.56 x_{8} & +  0.18 x_{9}\\
 x_{14}   &  32.8989637306 & -0.10 x_{12} & +  0.59 x_{16} & -6.53 x_{5} & + 12.39 x_{4} & -1.10 x_{13} & -12.67 x_{6} & -0.37 x_{7} & +  8.17 x_{8} & -10.81 x_{9}\\
 x_{15}   &  52.3160621762 & +  1.74 x_{12} & -0.87 x_{16} & -2.23 x_{5} & -4.23 x_{4} & -3.39 x_{13} & +  0.44 x_{6} & -15.80 x_{7} & + 28.43 x_{8} & +  3.82 x_{9}\\
 x_{10}   &  5.17357512953 & +  0.81 x_{12} & +  0.25 x_{16} & +  1.89 x_{5} & +  7.59 x_{4} & -1.64 x_{13} & +  1.82 x_{6} & -13.88 x_{7} & + 13.23 x_{8} & -7.43 x_{9}\\
 x_{17}   &  27.9766839378 & -1.41 x_{12} & +  0.98 x_{16} & -10.51 x_{5} & +  9.94 x_{4} & +  0.67 x_{13} & -10.16 x_{6} & +  0.22 x_{7} & -3.27 x_{8} & +  4.51 x_{9}\\
 x_{18}   &  44.5362694301 & +  0.35 x_{12} & +  0.42 x_{16} & -8.32 x_{5} & -5.51 x_{4} & +  0.63 x_{13} & -5.42 x_{6} & +  0.88 x_{7} & -3.80 x_{8} & +  4.38 x_{9}\\
\hline
z    &  8.01813471503 & -0.57 x_{12} & +  0.46 x_{16} & -5.16 x_{5} & -4.51 x_{4} & +  0.81 x_{13} & -4.21 x_{6} & +  0.94 x_{7} & -2.90 x_{8} & +  4.94 x_{9}\\
\end{array}\]


 $ x_{7} $ enters and $ x_{10} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{2}   &  1.94307577454 & +  0.05 x_{12} & -0.02 x_{16} & -0.87 x_{5} & -0.76 x_{4} & +  0.01 x_{13} & +  0.03 x_{6} & +  0.12 x_{10} & +  0.26 x_{8} & +  0.85 x_{9}\\
 x_{11}   &  20.5550578574 & -0.32 x_{12} & -0.79 x_{16} & +  4.11 x_{5} & -0.28 x_{4} & +  0.22 x_{13} & -8.96 x_{6} & +  0.47 x_{10} & -10.72 x_{8} & +  8.82 x_{9}\\
 x_{1}   &  0.247480403135 & -0.04 x_{12} & -0.02 x_{16} & +  0.42 x_{5} & +  0.48 x_{4} & -0.09 x_{13} & -0.61 x_{6} & +  0.00 x_{10} & +  0.52 x_{8} & -0.26 x_{9}\\
 x_{3}   &  1.94755505786 & -0.11 x_{12} & +  0.13 x_{16} & +  0.17 x_{5} & +  0.72 x_{4} & +  0.06 x_{13} & -0.33 x_{6} & -0.10 x_{10} & -0.22 x_{8} & -0.57 x_{9}\\
 x_{14}   &  32.7618514371 & -0.12 x_{12} & +  0.58 x_{16} & -6.58 x_{5} & + 12.18 x_{4} & -1.06 x_{13} & -12.72 x_{6} & +  0.03 x_{10} & +  7.82 x_{8} & -10.61 x_{9}\\
 x_{15}   &  46.4279581934 & +  0.82 x_{12} & -1.15 x_{16} & -4.38 x_{5} & -12.88 x_{4} & -1.52 x_{13} & -1.64 x_{6} & +  1.14 x_{10} & + 13.38 x_{8} & + 12.27 x_{9}\\
 x_{7}   &  0.372713699141 & +  0.06 x_{12} & +  0.02 x_{16} & +  0.14 x_{5} & +  0.55 x_{4} & -0.12 x_{13} & +  0.13 x_{6} & -0.07 x_{10} & +  0.95 x_{8} & -0.54 x_{9}\\
 x_{17}   &  28.0597237775 & -1.39 x_{12} & +  0.99 x_{16} & -10.48 x_{5} & + 10.06 x_{4} & +  0.64 x_{13} & -10.13 x_{6} & -0.02 x_{10} & -3.06 x_{8} & +  4.39 x_{9}\\
 x_{18}   &  44.8626353117 & +  0.41 x_{12} & +  0.43 x_{16} & -8.20 x_{5} & -5.03 x_{4} & +  0.52 x_{13} & -5.31 x_{6} & -0.06 x_{10} & -2.97 x_{8} & +  3.91 x_{9}\\
\hline
z    &  8.36767450541 & -0.52 x_{12} & +  0.48 x_{16} & -5.03 x_{5} & -3.99 x_{4} & +  0.70 x_{13} & -4.09 x_{6} & -0.07 x_{10} & -2.01 x_{8} & +  4.44 x_{9}\\
\end{array}\]


 $ x_{9} $ enters and $ x_{7} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{2}   &  2.53575165678 & +  0.14 x_{12} & +  0.01 x_{16} & -0.66 x_{5} & +  0.11 x_{4} & -0.18 x_{13} & +  0.24 x_{6} & +  0.01 x_{10} & +  1.77 x_{8} & -1.59 x_{7}\\
 x_{11}   &  26.7017788629 & +  0.64 x_{12} & -0.50 x_{16} & +  6.35 x_{5} & +  8.75 x_{4} & -1.73 x_{13} & -6.79 x_{6} & -0.72 x_{10} & +  4.99 x_{8} & -16.49 x_{7}\\
 x_{1}   &  0.0641785838856 & -0.07 x_{12} & -0.03 x_{16} & +  0.35 x_{5} & +  0.21 x_{4} & -0.03 x_{13} & -0.67 x_{6} & +  0.04 x_{10} & +  0.05 x_{8} & +  0.49 x_{7}\\
 x_{3}   &  1.55040111615 & -0.17 x_{12} & +  0.11 x_{16} & +  0.02 x_{5} & +  0.14 x_{4} & +  0.19 x_{13} & -0.47 x_{6} & -0.02 x_{10} & -1.24 x_{8} & +  1.07 x_{7}\\
 x_{14}   &  25.3686780607 & -1.27 x_{12} & +  0.23 x_{16} & -9.29 x_{5} & +  1.33 x_{4} & +  1.29 x_{13} & -15.33 x_{6} & +  1.46 x_{10} & -11.09 x_{8} & + 19.84 x_{7}\\
 x_{15}   &  54.975933031 & +  2.15 x_{12} & -0.74 x_{16} & -1.26 x_{5} & -0.33 x_{4} & -4.24 x_{13} & +  1.38 x_{6} & -0.51 x_{10} & + 35.23 x_{8} & -22.93 x_{7}\\
 x_{9}   &  0.69654691315 & +  0.11 x_{12} & +  0.03 x_{16} & +  0.25 x_{5} & +  1.02 x_{4} & -0.22 x_{13} & +  0.25 x_{6} & -0.13 x_{10} & +  1.78 x_{8} & -1.87 x_{7}\\
 x_{17}   &  31.1147540984 & -0.92 x_{12} & +  1.13 x_{16} & -9.36 x_{5} & + 14.54 x_{4} & -0.33 x_{13} & -9.05 x_{6} & -0.61 x_{10} & +  4.75 x_{8} & -8.20 x_{7}\\
 x_{18}   &  47.5877223579 & +  0.83 x_{12} & +  0.56 x_{16} & -7.21 x_{5} & -1.03 x_{4} & -0.34 x_{13} & -4.35 x_{6} & -0.59 x_{10} & +  4.00 x_{8} & -7.31 x_{7}\\
\hline
z    &  11.4593651901 & -0.04 x_{12} & +  0.62 x_{16} & -3.90 x_{5} & +  0.55 x_{4} & -0.28 x_{13} & -3.00 x_{6} & -0.67 x_{10} & +  5.90 x_{8} & -8.30 x_{7}\\
\end{array}\]


 $ x_{4} $ enters and $ x_{18} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{2}   &  7.71602434077 & +  0.23 x_{12} & +  0.07 x_{16} & -1.44 x_{5} & -0.11 x_{18} & -0.21 x_{13} & -0.24 x_{6} & -0.05 x_{10} & +  2.21 x_{8} & -2.39 x_{7}\\
 x_{11}   &  430.103448276 & +  7.68 x_{12} & +  4.26 x_{16} & -54.73 x_{5} & -8.48 x_{18} & -4.63 x_{13} & -43.66 x_{6} & -5.72 x_{10} & + 38.89 x_{8} & -78.47 x_{7}\\
 x_{1}   &  9.81338742394 & +  0.10 x_{12} & +  0.09 x_{16} & -1.13 x_{5} & -0.20 x_{18} & -0.10 x_{13} & -1.57 x_{6} & -0.08 x_{10} & +  0.87 x_{8} & -1.01 x_{7}\\
 x_{3}   &  7.95334685598 & -0.06 x_{12} & +  0.19 x_{16} & -0.95 x_{5} & -0.13 x_{18} & +  0.14 x_{13} & -1.06 x_{6} & -0.10 x_{10} & -0.70 x_{8} & +  0.08 x_{7}\\
 x_{14}   &  86.8884381339 & -0.20 x_{12} & +  0.96 x_{16} & -18.60 x_{5} & -1.29 x_{18} & +  0.85 x_{13} & -20.95 x_{6} & +  0.69 x_{10} & -5.92 x_{8} & + 10.38 x_{7}\\
 x_{15}   &  39.7890466531 & +  1.89 x_{12} & -0.92 x_{16} & +  1.04 x_{5} & +  0.32 x_{18} & -4.13 x_{13} & +  2.77 x_{6} & -0.33 x_{10} & + 33.95 x_{8} & -20.60 x_{7}\\
 x_{9}   &  47.8498985801 & +  0.93 x_{12} & +  0.59 x_{16} & -6.89 x_{5} & -0.99 x_{18} & -0.56 x_{13} & -4.06 x_{6} & -0.72 x_{10} & +  5.74 x_{8} & -9.11 x_{7}\\
 x_{17}   &  701.799188641 & + 10.78 x_{12} & +  9.06 x_{16} & -110.92 x_{5} & -14.09 x_{18} & -5.15 x_{13} & -70.34 x_{6} & -8.92 x_{10} & + 61.11 x_{8} & -111.24 x_{7}\\
 x_{4}   &  46.1237322515 & +  0.80 x_{12} & +  0.54 x_{16} & -6.98 x_{5} & -0.97 x_{18} & -0.33 x_{13} & -4.22 x_{6} & -0.57 x_{10} & +  3.88 x_{8} & -7.09 x_{7}\\
\hline
z    &  36.6206896552 & +  0.40 x_{12} & +  0.92 x_{16} & -7.71 x_{5} & -0.53 x_{18} & -0.46 x_{13} & -5.30 x_{6} & -0.98 x_{10} & +  8.01 x_{8} & -12.16 x_{7}\\
\end{array}\]


 $ x_{8} $ enters and $ x_{3} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{2}   &  32.8375241779 & +  0.05 x_{12} & +  0.67 x_{16} & -4.44 x_{5} & -0.53 x_{18} & +  0.23 x_{13} & -3.58 x_{6} & -0.38 x_{10} & -3.16 x_{3} & -2.13 x_{7}\\
 x_{11}   &  872.533365571 & +  4.48 x_{12} & + 14.72 x_{16} & -107.50 x_{5} & -15.96 x_{18} & +  3.23 x_{13} & -102.52 x_{6} & -11.51 x_{10} & -55.63 x_{3} & -73.92 x_{7}\\
 x_{1}   &  19.7127659574 & +  0.03 x_{12} & +  0.32 x_{16} & -2.31 x_{5} & -0.37 x_{18} & +  0.07 x_{13} & -2.88 x_{6} & -0.21 x_{10} & -1.24 x_{3} & -0.90 x_{7}\\
 x_{8}   &  11.3762088975 & -0.08 x_{12} & +  0.27 x_{16} & -1.36 x_{5} & -0.19 x_{18} & +  0.20 x_{13} & -1.51 x_{6} & -0.15 x_{10} & -1.43 x_{3} & +  0.12 x_{7}\\
 x_{14}   &  19.5618955513 & +  0.29 x_{12} & -0.63 x_{16} & -10.57 x_{5} & -0.15 x_{18} & -0.35 x_{13} & -11.99 x_{6} & +  1.57 x_{10} & +  8.47 x_{3} & +  9.69 x_{7}\\
 x_{15}   &  426.064796905 & -0.91 x_{12} & +  8.21 x_{16} & -45.03 x_{5} & -6.22 x_{18} & +  2.73 x_{13} & -48.63 x_{6} & -5.38 x_{10} & -48.57 x_{3} & -16.63 x_{7}\\
 x_{9}   &  113.188104449 & +  0.46 x_{12} & +  2.13 x_{16} & -14.68 x_{5} & -2.10 x_{18} & +  0.60 x_{13} & -12.76 x_{6} & -1.57 x_{10} & -8.22 x_{3} & -8.44 x_{7}\\
 x_{17}   &  1397.04400387 & +  5.76 x_{12} & + 25.49 x_{16} & -193.84 x_{5} & -25.86 x_{18} & +  7.21 x_{13} & -162.84 x_{6} & -18.02 x_{10} & -87.42 x_{3} & -104.09 x_{7}\\
 x_{4}   &  90.2171179884 & +  0.49 x_{12} & +  1.59 x_{16} & -12.24 x_{5} & -1.72 x_{18} & +  0.45 x_{13} & -10.08 x_{6} & -1.15 x_{10} & -5.54 x_{3} & -6.63 x_{7}\\
\hline
z    &  127.761121857 & -0.26 x_{12} & +  3.07 x_{16} & -18.58 x_{5} & -2.07 x_{18} & +  1.16 x_{13} & -17.42 x_{6} & -2.17 x_{10} & -11.46 x_{3} & -11.22 x_{7}\\
\end{array}\]


 $ x_{13} $ enters and $ x_{14} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{2}   &  45.8787878788 & +  0.24 x_{12} & +  0.24 x_{16} & -11.48 x_{5} & -0.64 x_{18} & -0.67 x_{14} & -11.58 x_{6} & +  0.67 x_{10} & +  2.48 x_{3} & +  4.33 x_{7}\\
 x_{11}   &  1052.44352617 & +  7.16 x_{12} & +  8.89 x_{16} & -204.73 x_{5} & -17.38 x_{18} & -9.20 x_{14} & -212.83 x_{6} & +  2.97 x_{10} & + 22.23 x_{3} & + 15.21 x_{7}\\
 x_{1}   &  23.8622589532 & +  0.09 x_{12} & +  0.18 x_{16} & -4.55 x_{5} & -0.40 x_{18} & -0.21 x_{14} & -5.43 x_{6} & +  0.12 x_{10} & +  0.55 x_{3} & +  1.15 x_{7}\\
 x_{8}   &  22.6391184573 & +  0.09 x_{12} & -0.10 x_{16} & -7.44 x_{5} & -0.28 x_{18} & -0.58 x_{14} & -8.42 x_{6} & +  0.76 x_{10} & +  3.44 x_{3} & +  5.70 x_{7}\\
 x_{13}   &  55.7217630854 & +  0.83 x_{12} & -1.81 x_{16} & -30.11 x_{5} & -0.44 x_{18} & -2.85 x_{14} & -34.16 x_{6} & +  4.48 x_{10} & + 24.11 x_{3} & + 27.61 x_{7}\\
 x_{15}   &  578.41046832 & +  1.36 x_{12} & +  3.27 x_{16} & -127.36 x_{5} & -7.41 x_{18} & -7.79 x_{14} & -142.03 x_{6} & +  6.88 x_{10} & + 17.36 x_{3} & + 58.85 x_{7}\\
 x_{9}   &  146.680440771 & +  0.96 x_{12} & +  1.05 x_{16} & -32.78 x_{5} & -2.36 x_{18} & -1.71 x_{14} & -33.29 x_{6} & +  1.12 x_{10} & +  6.28 x_{3} & +  8.15 x_{7}\\
 x_{17}   &  1798.65564738 & + 11.73 x_{12} & + 12.46 x_{16} & -410.88 x_{5} & -29.01 x_{18} & -20.53 x_{14} & -409.07 x_{6} & + 14.30 x_{10} & + 86.38 x_{3} & + 94.88 x_{7}\\
 x_{4}   &  115.41046832 & +  0.86 x_{12} & +  0.77 x_{16} & -25.86 x_{5} & -1.91 x_{18} & -1.29 x_{14} & -25.53 x_{6} & +  0.88 x_{10} & +  5.36 x_{3} & +  5.85 x_{7}\\
\hline
z    &  192.374655647 & +  0.71 x_{12} & +  0.98 x_{16} & -53.50 x_{5} & -2.58 x_{18} & -3.30 x_{14} & -57.04 x_{6} & +  3.03 x_{10} & + 16.50 x_{3} & + 20.79 x_{7}\\
\end{array}\]


 $ x_{3} $ enters and Unbounded Dictionary!


 $ x_{3} $ enters and Unbounded Dictionary!
\end{document}
